12.22 Precision Math

MySQL provides support for precision math: numeric value handling
that results in extremely accurate results and a high degree control
over invalid values. Precision math is based on these two features:

SQL modes that control how strict the server is about accepting
or rejecting invalid data.

The MySQL library for fixed-point arithmetic.

These features have several implications for numeric operations and
provide a high degree of compliance with standard SQL:

Precise calculations: For
exact-value numbers, calculations do not introduce
floating-point errors. Instead, exact precision is used. For
example, MySQL treats a number such as .0001
as an exact value rather than as an approximation, and summing
it 10,000 times produces a result of exactly
1, not a value that is merely
“close” to 1.

Well-defined rounding behavior:
For exact-value numbers, the result of
ROUND() depends on its argument,
not on environmental factors such as how the underlying C
library works.

Platform independence:
Operations on exact numeric values are the same across different
platforms such as Windows and Unix.

Control over handling of invalid
values: Overflow and division by zero are detectable
and can be treated as errors. For example, you can treat a value
that is too large for a column as an error rather than having
the value truncated to lie within the range of the column's data
type. Similarly, you can treat division by zero as an error
rather than as an operation that produces a result of
NULL. The choice of which approach to take is
determined by the setting of the server SQL mode.

The following discussion covers several aspects of how precision
math works, including possible incompatibilities with older
applications. At the end, some examples are given that demonstrate
how MySQL handles numeric operations precisely. For information
about controlling the SQL mode, see Section 5.1.10, “Server SQL Modes”.